Question

9. If x^a = y^b = (xy)^c show that ab =
c(a+b)​

Answer 1

Step-by-step explanation:

let, x^a =y^b =(xy)^c =k

so, x =k^1/a -----------(i)

y= k^1/b ---------(ii)

xy= k^1/c --------(iii)

from (i),(ii) and (iii) we get

k^1/a ×k^1/b =k^1/c

or, k^(1/a+1/b) = k^1/c

or, 1/a + 1/b = 1/c

or, (a + b)/ab = 1/c

or c(a+b) = ab (proved)